Chapter 2.3, Problem 7P

An outdoor swimming pool loses $0.05\%$ of its water volume every day it is in use, due to losses from excited swimmers who splash water and from evaporation. A system is available to continually replace water at a rate of $G$ gallons per day of use.

Find an expression, in terms of $G$, for the equilibrium volume of the pool. Sketch a few graphs for the volume $V\left(t\right)$, including all possible types of solutions.

If the pool volume is initially $1\%$ above its equilibrium value, find an expression for $V\left(t\right)$.

What is the replacement rate $G$ required to maintain $12,000$ gal of water in the pool?